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On the space of rhythms of arbitrary length with a fixed number of onsets, aself map $F$ is constructed. It is shown that for any rhythm $\mathbf{r}$ ofthe space there exists a nonnegative integer $k$ such that $F^k(\mathbf{r})$falls into the category of "maximally even rhythms" investigated in [1].

Iterative method of construction of good rhythms